High-order compact scheme for solving nonlinear Black-Scholes equation with transaction cost

Authors:
Wenyuan Liao;Abdul Q. M. Khaliq
Affiliations:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada;Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, Tennessee, USA
Venue:
International Journal of Computer Mathematics - SPECIAL ISSUE ON FINANCIAL DERIVATIVES
Year:
2009

Citing 3
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Abstract

In this paper, an unconditionally stable high-order compact finite difference scheme is proposed. The compact scheme is fourth-order accurate in both the temporal and spatial dimensions. The new method computes both the option price and the hedging delta ∂ V/∂ S simultaneously. Two numerical examples are presented to demonstrate the accuracy and efficiency of the proposed scheme.